Recently, the strain-smoothed element (SSE) method has been developed for 3-node triangular and 4-node tetrahedral solid elements. The method was also applied for enhancing the membrane performance of a 3-node triangular shell element (MITC3+ element). Using the SSE method, convergence behaviors of the finite elements were significantly improved without additional degrees of freedom. However, the application of the SSE method is limited to constant strain finite elements such as 3-node triangular and 4-node tetrahedral elements. In this paper, the SSE method is applied to a 4-node quadrilateral finite element. Doing so, the piecewise linear shape functions are employed instead of standard bilinear shape functions. The proposed strain-smoothed 4-node quadrilateral element passes all the basic tests, and shows a significantly improved accuracy in various numerical examples.